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** Exterior Angles in a Triangle ** y2kcenter.org Topical Outline | Geometry Outline | MathBits” Teacher Resources **Terms of Use Contact Person:** Donna Roberts

An exterior angle of a triangle is an angle formed by one side of the triangle and the extension of an adjacent side of the triangle.

**FACTS:** • Every triangle has 6 exterior angles, two at each vertex.• Angles 1 through 6 are exterior angles.• Notice that the “outside” angles that are “vertical” to the angles inside the triangle are NOT called exterior angles of a triangle.

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The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. (Non-adjacent interior angles may also be referred to as remote interior angles.)

**FACTS:** • An exterior ∠ is equal to the addition of the two Δ angles not right next to it. 140º = 60º + 80º; 120º = 80º + 40º; 100º = 60º + 40º • An exterior angle is supplementary to its adjacent Δ angle. 140º is supp to 40º • The 2 exterior angles at each vertex are = in measure because they are vertical angles. • The exterior angles (taken one at a vertex) always total 360º

*Solution: Using the Exterior Angle Theorem*** 145 = 80 + x x = 65 Now, if you forget the Exterior Angle Theorem, you can still get the answer by noticing that a straight angle has been formed at the vertex of the 145º angle. See Example 2. **

Solution: I forgot the Exterior Angle Theorem. The angle adjacent to 145º will form a straight angle along with 145º adding to 180º. That angle is 35º. Now use rule that sum of ∠s in Δ = 180º. 35 + 80 + x = 180 115 + x = 180 x = 65

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Find m∠DBC.** Solution:***∠BDC* is an exterior angle for Δ*ABD*. *m∠BDC* = 35 + 25 *m∠BDC* = 60º 180* = m∠DBC* + 60 + 60 *m∠DBC* = 60º